@article{3003,
  abstract     = {Plant development displays an exceptional plasticity and adaptability that involves the dynamic, asymmetric distribution of the phytohormone auxin. Polar auxin flow, which requires polarly localized transport facilitators of the PIN family, largely contributes to the establishment and maintenance of the auxin gradients. Functionally overlapping action of PIN proteins mediates multiple developmental processes, including embryo formation, organ development and tropisms. Here we show that PIN proteins exhibit synergistic interactions, which involve cross-regulation of PIN gene expression in pin mutants or plants with inhibited auxin transport. Auxin itself positively feeds back on PIN gene expression in a tissue-specific manner through an AUX/IAA-dependent signalling pathway. This regulatory switch is indicative of a mechanism by which the loss of a specific PIN protein is compensated for by auxin-dependent ectopic: expression of its homologues. The compensatory properties of the PIN-dependent transport network might enable the stabilization of auxin gradients and potentially contribute to the robustness of plant adaptive development.},
  author       = {Vieten, Anne and Vanneste, Steffen and Wiśniewska, Justyna and Eva Benková and Benjamins, René and Beeckman, Tom and Luschnig, Christian and Jirí Friml},
  journal      = {Development},
  number       = {20},
  pages        = {4521 -- 4531},
  publisher    = {Company of Biologists},
  title        = {{Functional redundancy of PIN proteins is accompanied by auxin-dependent cross-regulation of PIN expression}},
  doi          = {10.1242/dev.02027},
  volume       = {132},
  year         = {2005},
}

@article{3004,
  abstract     = {Molecular mechanisms of pattern formation in the plant embryo are not well understood. Recent molecular and cellular studies, in conjunction with earlier microsurgical, physiological, and genetic work, are now starting to define the outlines of a model where gradients of the signaling molecule auxin play a central role in embryo patterning. It is relatively clear how these gradients are established and interpreted, but how they are maintained is still unresolved. Here, we have studied the contributions of auxin biosynthesis, conjugation, and transport pathways to the maintenance of embryonic auxin gradients. Auxin homeostasis in the embryo was manipulated by region-specific conditional expression of indoleacetic acid-tryptophan monooxygenase or indoleacetic acid-lysine synthetase, bacterial enzymes for auxin biosynthesis or conjugation. Neither manipulation of auxin biosynthesis nor of auxin conjugation interfered with auxin gradients and patterning in the embryo. This result suggests a compensatory mechanism for buffering auxin gradients in the embryo. Chemical and genetic inhibition revealed that auxin transport activity, in particular that of the PIN-FORMED1 (PIN1) and PIN4 proteins, is a major factor in the maintenance of these gradients.},
  author       = {Weijers, Dolf and Sauer, Michael and Meurette, Olivier and Jirí Friml and Ljung, Karin and Sandberg, Göran and Hooykaas, Paul and Offringa, Remko},
  journal      = {Plant Cell},
  number       = {9},
  pages        = {2517 -- 2526},
  publisher    = {American Society of Plant Biologists},
  title        = {{Maintenance of embryonic auxin distribution for apical basal patterning by PIN FORMED dependent auxin transport in Arabidopsis}},
  doi          = {10.1105/tpc.105.034637},
  volume       = {17},
  year         = {2005},
}

@article{3141,
  abstract     = {The two actin-related subunits of the Arp2/3 complex, Arp2 and Arp3, are proposed to form a pseudo actin dimer that nucleates actin polymerization. However, in the crystal structure of the inactive complex, they are too far apart to form such a nucleus. Here, we show using EM that yeast and bovine Arp2/3 complexes exist in a distribution among open, intermediate and closed conformations. The crystal structure docks well into the open conformation. The activator WASp binds at the cleft between Arp2 and Arp3, and all WASp-bound complexes are closed. The inhibitor coronin binds near the p35 subunit, and all coronin-bound complexes are open. Activating and loss-of-function mutations in the p35 subunit skew conformational distribution in opposite directions, closed and open, respectively. We conclude that WASp stabilizes p35-dependent closure of the complex, holding Arp2 and Arp3 closer together to nucleate an actin filament.},
  author       = {Rodal, Avital A and Sokolova, Olga and Robins, Deborah B and Daugherty, Karen M and Simon Hippenmeyer and Riezman, Howard and Grigorieff, Nikolaus and Goode, Bruce L},
  journal      = {Nature Structural and Molecular Biology},
  number       = {1},
  pages        = {26 -- 31},
  publisher    = {Nature Publishing Group},
  title        = {{Conformational changes in the Arp2 3 complex leading to actin nucleation}},
  doi          = {10.1038/nsmb870},
  volume       = {12},
  year         = {2005},
}

@article{3143,
  abstract     = {Two ETS transcription factors of the Pea3 subfamily are induced in subpopulations of dorsal root ganglion (DRG) sensory and spinal motor neurons by target-derived factors. Their expression controls late aspects of neuronal differentiation such as target invasion and branching. Here, we show that the late onset of ETS gene expression is an essential requirement for normal sensory neuron differentiation. We provide genetic evidence in the mouse that precocious ETS expression in DRG sensory neurons perturbs axonal projections, the acquisition of terminal differentiation markers, and their dependence on neurotrophic support. Together, our findings indicate that DRG sensory neurons exhibit a temporal developmental switch that can be revealed by distinct responses to ETS transcription factor signaling at sequential steps of neuronal maturation.},
  author       = {Simon Hippenmeyer and Vrieseling, Eline and Sigrist, Markus and Portmann, Thomas and Laengle, Celia and Ladle, David R and Arber, Silvia},
  journal      = {PLoS Biology},
  number       = {5},
  pages        = {0878 -- 0890},
  publisher    = {Public Library of Science},
  title        = {{A developmental switch in the response of DRG neurons to ETS transcription factor signaling}},
  doi          = {10.1371/journal.pbio.0030159},
  volume       = {3},
  year         = {2005},
}

@inproceedings{3175,
  abstract     = {This paper addresses the novel problem of automatically synthesizing an output image from a large collection of different input images. The synthesized image, called a digital tapestry, can be viewed as a visual summary or a virtual 'thumbnail' of all the images in the input collection. The problem of creating the tapestry is cast as a multi-class labeling problem such that each region in the tapestry is constructed from input image blocks that are salient and such that neighboring blocks satisfy spatial compatibility. This is formulated using a Markov Random Field and optimized via the graph cut based expansion move algorithm. The standard expansion move algorithm can only handle energies with metric terms, while our energy contains non-metric (soft and hard) constraints. Therefore we propose two novel contributions. First, we extend the expansion move algorithm for energy functions with non-metric hard constraints. Secondly, we modify it for functions with "almost" metric soft terms, and show that it gives good results in practice. The proposed framework was tested on several consumer photograph collections, and the results are presented.},
  author       = {Rother, Carsten and Kumar, Sanjiv and Vladimir Kolmogorov and Blake, Andrew},
  pages        = {589 -- 596},
  publisher    = {IEEE},
  title        = {{Digital tapestry}},
  doi          = {10.1109/CVPR.2005.130},
  volume       = {1},
  year         = {2005},
}

@inproceedings{3176,
  abstract     = {This paper demonstrates the high quality, real-time segmentation techniques. We achieve real-time segmentation of foreground from background layers in stereo video sequences. Automatic separation of layers from colour/contrast or from stereo alone is known to be error-prone. Here, colour, contrast and stereo matching information are fused to infer layers accurately and efficiently. The first algorithm, layered dynamic programming (LDP), solves stereo in an extended 6-state space that represents both foreground/background layers and occluded regions. The stereo-match likelihood is then fused with a contrast-sensitive colour model that is learned on the fly, and stereo disparities are obtained by dynamic programming. The second algorithm, layered graph cut (LGC), does not directly solve stereo. Instead the stereo match likelihood is marginalised over foreground and background hypotheses, and fused with a contrast-sensitive colour model like the one used in LDP. Segmentation is solved efficiently by ternary graph cut. Both algorithms are evaluated with respect to ground truth data and found to have similar performance, substantially better than stereo or colour/contrast alone. However, their characteristics with respect to computational efficiency are rather different. The algorithms are demonstrated in the application of background substitution and shown to give good quality composite video output.
},
  author       = {Vladimir Kolmogorov and Criminisi, Antonio and Blake, Andrew and Cross, Geoffrey and Rother, Carsten},
  pages        = {1186 -- 1186},
  publisher    = {IEEE},
  title        = {{Bi-layer segmentation of binocular stereo video}},
  doi          = {10.1109/CVPR.2005.90},
  year         = {2005},
}

@inproceedings{3181,
  abstract     = {Tree-reweighted max-product (TRW) message passing [9] is a modified form of the ordinary max-product algorithm for attempting to find minimal energy configurations in Markov random field with cycles. For a TRW fixed point satisfying the strong tree agreement condition, the algorithm outputs a configuration that is provably optimal. In this paper, we focus on the case of binary variables with pairwise couplings, and establish stronger properties of TRW fixed points that satisfy only the milder condition of weak tree agreement (WTA). First, we demonstrate how it is possible to identify part of the optimal solution - i.e., a provably optimal solution for a subset of nodes - without knowing a complete solution. Second, we show that for submodular functions, a WTA fixed point always yields a globally optimal solution. We establish that for binary variables, any WTA fixed point always achieves the global maximum of the linear programming relaxation underlying the TRW method.},
  author       = {Vladimir Kolmogorov and Wainwright, Martin J},
  pages        = {316 -- 323},
  publisher    = {AUAI Press},
  title        = {{On the optimality of tree reweighted max product message passing}},
  year         = {2005},
}

@inproceedings{3182,
  abstract     = {In the work of the authors (2003), we showed that graph cuts can find hypersurfaces of globally minimal length (or area) under any Riemannian metric. Here we show that graph cuts on directed regular grids can approximate a significantly more general class of continuous non-symmetric metrics. Using submodularity condition (Boros and Hammer, 2002 and Kolmogorov and Zabih, 2004), we obtain a tight characterization of graph-representable metrics. Such "submodular" metrics have an elegant geometric interpretation via hypersurface functionals combining length/area and flux. Practically speaking, we attend 'geo-cuts' algorithm to a wider class of geometrically motivated hypersurface functionals and show how to globally optimize any combination of length/area and flux of a given vector field. The concept of flux was recently introduced into computer vision by Vasilevskiy and Siddiqi (2002) but it was mainly studied within variational framework so far. We are first to show that flux can be integrated into graph cuts as well. Combining geometric concepts of flux and length/area within the global optimization framework of graph cuts allows principled discrete segmentation models and advances the slate of the art for the graph cuts methods in vision. In particular we address the "shrinking" problem of graph cuts, improve segmentation of long thin objects, and introduce useful shape constraints.},
  author       = {Vladimir Kolmogorov and Boykov, Yuri},
  pages        = {564 -- 571},
  publisher    = {IEEE},
  title        = {{What metrics can be approximated by geo cuts or global optimization of length area and flux}},
  doi          = {10.1109/ICCV.2005.252},
  volume       = {1},
  year         = {2005},
}

@inproceedings{3183,
  abstract     = {This paper describes two algorithms capable of real-time segmentation of foreground from background layers in stereo video sequences. Automatic separation of layers from colour/contrast or from stereo alone is known to be error-prone. Here, colour, contrast and stereo matching information are fused to infer layers accurately and efficiently. The first algorithm, Layered Dynamic Programming (LDP), solves stereo in an extended 6-state space that represents both foreground/background layers and occluded regions. The stereo-match likelihood is then fused with a contrast-sensitive colour model that is learned on the fly, and stereo disparities are obtained by dynamic programming. The second algorithm, Layered Graph Cut (LGC), does not directly solve stereo. Instead the stereo match likelihood is marginalised over foreground and background hypotheses, and fused with a contrast-sensitive colour model like the one used in LDP. Segmentation is solved efficiently by ternary graph cut. Both algorithms are evaluated with respect to ground truth data and found to have similar perfomance, substantially better than stereo or colour/contrast alone. However, their characteristics with respect to computational efficiency are rather different. The algorithms are demonstrated in the application of background substitution and shown to give good quality composite video output.},
  author       = {Vladimir Kolmogorov and Criminisi, Antonio and Blake, Andrew and Cross, Geoffrey and Rother, Carsten},
  pages        = {407 -- 414},
  publisher    = {IEEE},
  title        = {{Bi-layer segmentation of binocular stereo video}},
  doi          = {10.1109/CVPR.2005.91},
  volume       = {2},
  year         = {2005},
}

@inproceedings{3211,
  abstract     = {We present an improved bound on the advantage of any q-query adversary at distinguishing between the CBC MAC over a random n-bit permutation and a random function outputting n bits. The result assumes that no message queried is a prefix of any other, as is the case when all messages to be MACed have the same length. We go on to give an improved analysis of the encrypted CBC MAC, where there is no restriction on queried messages. Letting m be the block length of the longest query, our bounds are about mq2/2n for the basic CBC MAC and mo(1)q2/2n for the encrypted CBC MAC, improving prior bounds of m2q2/2n. The new bounds translate into improved guarantees on the probability of forging these MACs.},
  author       = {Bellare, Mihir and Krzysztof Pietrzak and Rogaway, Phillip},
  pages        = {527 -- 545},
  publisher    = {Springer},
  title        = {{Improved security analyses for CBC MACs}},
  doi          = {10.1007/11535218_32},
  volume       = {3621},
  year         = {2005},
}

@inproceedings{3212,
  abstract     = {The Full-Domain Hash (FDH) signature scheme [3] forms one the most basic usages of random oracles. It works with a family F of trapdoor permutations (TDP), where the signature of m is computed as f−1(h(m)) (here f ∈R F and h is modelled as a random oracle). It is known to be existentially unforgeable for any TDP family F [3], although a much tighter security reduction is known for a restrictive class of TDP’s [10,14] — namely, those induced by a family of claw-free permutations (CFP) pairs. The latter result was shown [11] to match the best possible “black-box” security reduction in the random oracle model, irrespective of the TDP family F (e.g., RSA) one might use.
In this work we investigate the question if it is possible to instantiate the random oracle h with a “real” family of hash functions H such that the corresponding schemes can be proven secure in the standard model, under some natural assumption on the family F. Our main result rules out the existence of such instantiations for any assumption on F which (1) is satisfied by a family of random permutations; and (2) does not allow the attacker to invert f ∈R F on an a-priori unbounded number of points. Moreover, this holds even if the choice of H can arbitrarily depend on f. As an immediate corollary, we rule out instantiating FDH based on general claw-free permutations, which shows that in order to prove the security of FDH in the standard model one must utilize significantly more structure on F than what is sufficient for the best proof of security in the random oracle model.},
  author       = {Dodis, Yevgeniy and Oliveira, Roberto and Krzysztof Pietrzak},
  pages        = {449 -- 466},
  publisher    = {Springer},
  title        = {{On the generic insecurity of the full domain hash}},
  doi          = {10.1007/11535218_27},
  volume       = {3621},
  year         = {2005},
}

@inproceedings{3213,
  abstract     = {We study the question whether the sequential or parallel composition of two functions, each indistinguishable from a random function by non-adaptive distinguishers is secure against adaptive distinguishers. The sequential composition of F and G is the function G(F()), the parallel composition is F G where ⋆ is some group operation. It has been shown that composition indeed gives adaptive security in the information theoretic setting, but unfortunately the proof does not translate into the more interesting computational case.
In this work we show that in the computational setting composition does not imply adaptive security: If there is a prime order cyclic group where the decisional Diffie-Hellman assumption holds, then there are functions F and G which are indistinguishable by non-adaptive polynomially time-bounded adversaries, but whose parallel composition can be completely broken (i.e. we recover the key) with only three adaptive queries. We give a similar result for sequential composition. Interestingly, we need a standard assumption from the asymmetric (aka. public-key) world to prove a negative result for symmetric (aka. private-key) systems.},
  author       = {Krzysztof Pietrzak},
  pages        = {55 -- 65},
  publisher    = {Springer},
  title        = {{Composition does not imply adaptive security}},
  doi          = {10.1007/11535218_4},
  volume       = {3621},
  year         = {2005},
}

@article{3416,
  abstract     = {In the last decade atomic force microscopy has been used to measure the mechanical stability of single proteins. These force spectroscopy experiments have shown that many water-soluble and membrane proteins unfold via one or more intermediates. Recently, Li and co-workers found a linear correlation between the unfolding force of the native state and the intermediate in fibronectin, which they suggested indicated the presence of a molecular memory or multiple unfolding pathways (1). Here, we apply two independent methods in combination with Monte Carlo simulations to analyze the unfolding of α-helices E and D of bacteriorhodopsin (BR). We show that correlation analysis of unfolding forces is very sensitive to errors in force calibration of the instrument. In contrast, a comparison of relative forces provides a robust measure for the stability of unfolding intermediates. The proposed approach detects three energetically different states of α-helices E and D in trimeric BR. These states are not observed for monomeric BR and indicate that substantial information is hidden in forced unfolding experiments of single proteins.},
  author       = {Harald Janovjak and Sapra, Tanuj K and Mueller, Daniel J},
  journal      = {Biophysical Journal},
  number       = {5},
  pages        = {37 -- 39},
  publisher    = {Biophysical Society},
  title        = {{Complex stability of single proteins explored by forced unfolding experiments}},
  doi          = {10.1529/biophysj.105.059774},
  volume       = {88},
  year         = {2005},
}

@article{3417,
  abstract     = {Recently, direct measurements of forces stabilizing single proteins or individual receptor–ligand bonds became possible with ultra-sensitive force probe methods like the atomic force microscope (AFM). In force spectroscopy experiments using AFM, a single molecule or receptor–ligand pair is tethered between the tip of a micromachined cantilever and a supporting surface. While the molecule is stretched, forces are measured by the deflection of the cantilever and plotted against extension, yielding a force spectrum characteristic for each biomolecular system. In order to obtain statistically relevant results, several hundred to thousand single-molecule experiments have to be performed, each resulting in a unique force spectrum. We developed software and algorithms to analyse large numbers of force spectra. Our algorithms include the fitting polymer extension models to force peaks as well as the automatic alignment of spectra. The aligned spectra allowed recognition of patterns of peaks across different spectra. We demonstrate the capabilities of our software by analysing force spectra that were recorded by unfolding single transmembrane proteins such as bacteriorhodopsin and NhaA. Different unfolding pathways were detected by classifying peak patterns. Deviant spectra, e.g. those with no attachment or erratic peaks, can be easily identified. The software is based on the programming language C++, the GNU Scientific Library (GSL), the software WaveMetrics IGOR Pro and available open-source at http://bioinformatics.org/fskit/.},
  author       = {Kuhn, Michael and Harald Janovjak and Hubain, Maurice and Mueller, Daniel J},
  journal      = {Journal of Microscopy},
  number       = {2},
  pages        = {125 -- 132},
  publisher    = {Wiley-Blackwell},
  title        = {{Automated alignment and pattern recognition of single-molecule force spectroscopy data}},
  doi          = {10.1111/j.1365-2818.2005.01478.x},
  volume       = {218},
  year         = {2005},
}

@article{3418,
  abstract     = {Atomic force microscopy (AFM) allows the critical forces that unfold single proteins and rupture individual receptor–ligand bonds to be measured. To derive the shape of the energy landscape, the dynamic strength of the system is probed at different force loading rates. This is usually achieved by varying the pulling speed between a few nm/s and a few mgrm/s, although for a more complete investigation of the kinetic properties higher speeds are desirable. Above 10 mgrm/s, the hydrodynamic drag force acting on the AFM cantilever reaches the same order of magnitude as the molecular forces. This has limited the maximum pulling speed in AFM single-molecule force spectroscopy experiments. Here, we present an approach for considering these hydrodynamic effects, thereby allowing a correct evaluation of AFM force measurements recorded over an extended range of pulling speeds (and thus loading rates). To support and illustrate our theoretical considerations, we experimentally evaluated the mechanical unfolding of a multi-domain protein recorded at 30 mgrm/s pulling speed.},
  author       = {Harald Janovjak and Struckmeier, Jens and Mueller, Daniel J},
  journal      = {European Biophysics Journal},
  number       = {1},
  pages        = {91 -- 96},
  publisher    = {Springer},
  title        = {{Hydrodynamic effects in fast AFM single molecule force measurements}},
  doi          = {10.1007/s00249-004-0430-3},
  volume       = {34},
  year         = {2005},
}

@article{13431,
  abstract     = {Hydrogel stamps can microstructure solid surfaces, i.e., modify the surface topology of metals, glasses, and crystals. It is demonstrated that stamps soaked in an appropriate etchant can remove material with micrometer-scale precision. The Figure shows an array of concentric circles etched in glass using the immersion wet stamping process described (scale bar: 500 μm).},
  author       = {Smoukov, S. K. and Bishop, K. J. M. and Klajn, Rafal and Campbell, C. J. and Grzybowski, B. A.},
  issn         = {1521-4095},
  journal      = {Advanced Materials},
  keywords     = {Mechanical Engineering, Mechanics of Materials, General Materials Science},
  number       = {11},
  pages        = {1361--1365},
  publisher    = {Wiley},
  title        = {{Cutting into solids with micropatterned gels}},
  doi          = {10.1002/adma.200402086},
  volume       = {17},
  year         = {2005},
}

@article{13432,
  abstract     = {A new experimental technique is described that uses reaction−diffusion phenomena as a means of one-step microfabrication of complex, multilevel surface reliefs. Thin films of dry gelatin doped with potassium hexacyanoferrate are chemically micropatterned with a solution of silver nitrate delivered from an agarose stamp. Precipitation reaction between the two salts causes the surface to deform. The mechanism of surface deformation is shown to involve a sequence of reactions, diffusion, and gel swelling/contraction. This mechanism is established experimentally and provides a basis of a theoretical lattice-gas model that allows prediction surface topographies emerging from arbitrary geometries of the stamped features. The usefulness of the technique is demonstrated by using it to rapidly prepare two types of mold for passive microfluidic mixers.},
  author       = {Campbell, Christopher J. and Klajn, Rafal and Fialkowski, Marcin and Grzybowski, Bartosz A.},
  issn         = {1520-5827},
  journal      = {Langmuir},
  keywords     = {Electrochemistry, Spectroscopy, Surfaces and Interfaces, Condensed Matter Physics, General Materials Science},
  number       = {1},
  pages        = {418--423},
  publisher    = {American Chemical Society},
  title        = {{One-step multilevel microfabrication by reaction−diffusion}},
  doi          = {10.1021/la0487747},
  volume       = {21},
  year         = {2005},
}

@article{13433,
  abstract     = {Self-assembled monolayers (SAMs) of alkane thiols on gold and other metals are versatile constructs with which to study interfacial phenomena and reactions at surfaces. Surface properties of SAMs - e.g., wettability, stability in diverse environments, propensity to interact with or to resist adsorption of macromolecules -- depend on and can be controlled flexibly by the properties of the functional (head) groups in the w position of the alkyl chain. SAMs provide a basis for many important scientific and technological applications, ranging from micropatterning methods, through sensing, to biological recognition. Despite their importance, the literature on SAMs and the synthesis of molecules that constitute them remains scattered and often conflicting. The purpose of this Review is (i) to summarize the applications and physical properties of SAMs and (ii) to systematize the strategies of synthesis of ω-functionalized alkane thiols. Generic retrosynthetic scheme is developed that allows efficient synthetic planning. Issues related to the selection of appropriate protecting groups and the ways of introduction of the thiol functionality are discussed in detail, and illustrated with examples of syntheses of several complex alkane thiols.},
  author       = {Witt, Dariusz and Klajn, Rafal and Barski, Piotr and Grzybowski, Bartosz},
  issn         = {1875-5348},
  journal      = {Current Organic Chemistry},
  keywords     = {Organic Chemistry},
  number       = {18},
  pages        = {1763--1797},
  publisher    = {Bentham Science},
  title        = {{Applications, properties and synthesis of w-functionalized n-alkanethiols and disulfides - the building blocks of self-assembled monolayers}},
  doi          = {10.2174/1385272043369421},
  volume       = {8},
  year         = {2005},
}

@inbook{1444,
  abstract     = {The paper surveys the mirror symmetry conjectures of Hausel-Thaddeus and Hausel-Rodriguez-Villegas concerning the equality of certain Hodge numbers of SL(n, ℂ) vs. PGL(n, ℂ) flat connections and character varieties for curves, respectively. Several new results and conjectures and their relations to works of Hitchin, Gothen, Garsia-Haiman and Earl-Kirwan are explained. These use the representation theory of finite groups of Lie-type via the arithmetic of character varieties and lead to an unexpected conjecture for a Hard Lefschetz theorem for their cohomology.},
  author       = {Tamas Hausel},
  booktitle    = {Geometric Methods in Algebra and Number Theory},
  pages        = {193 -- 217},
  publisher    = {Springer},
  title        = {{Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve}},
  doi          = {10.1007/0-8176-4417-2_9},
  volume       = {235},
  year         = {2005},
}

@article{1447,
  abstract     = {Building on a recent paper [8], here we argue that the combinatorics of matroids are intimately related to the geometry and topology of toric hyperkähler varieties. We show that just like toric varieties occupy a central role in Stanley’s proof for the necessity of McMullen’s conjecture (or g-inequalities) about the classification of face vectors of simplicial polytopes, the topology of toric hyperkähler varieties leads to new restrictions on face vectors of matroid complexes. Namely in this paper we will give two proofs that the injectivity part of the Hard Lefschetz theorem survives for toric hyperkähler varieties. We explain how this implies the g-inequalities for rationally representable matroids. We show how the geometrical intuition in the first proof, coupled with results of Chari [3], leads to a proof of the g-inequalities for general matroid complexes, which is a recent result of Swartz [20]. The geometrical idea in the second proof will show that a pure O-sequence should satisfy the g-inequalities, thus showing that our result is in fact a consequence of a long-standing conjecture of Stanley.},
  author       = {Tamas Hausel},
  journal      = {Open Mathematics},
  number       = {1},
  pages        = {26 -- 38},
  publisher    = {Central European Science Journals},
  title        = {{Quaternionic geometry of matroids}},
  doi          = {10.2478/BF02475653},
  volume       = {3},
  year         = {2005},
}